The London EMA would be based mainly on redirecting existing funds in colleges and the capital's universities. This includes the bursary fund the government introduced to replace the EMA and money spent on outreach activities by London universities.

Livingstone's campaign team say local authorities will also be asked to contribute, and it may be topped up from the Greater London Authority's budget.

He said: "I want to help young Londoners with their education by easing the squeeze the Tory-led government has imposed on them, and which the Tory mayor has totally ignored.

"I have been deeply struck by the plight of thousands of students I have met at colleges right across the capital, who have had the lifeline that EMA offered snatched away from them by the Conservative party, whilst the part-time Tory mayor stood by."

The initiative has been backed by the Labour leader of Lambeth council, Steve Reed, who said in a statement: "The government's cuts to EMA have caused real hardship for young Londoners. Ken's plan to reverse the cuts to EMA will make a massive difference to the lives of thousands of young Londoners, giving them the chance to learn and make the most of their potential."

About half a dozen other Labour-led councils have agreed to support the plan, according to Livingstone's team.

London Higher, the umbrella group for London universities, has also been approached to contribute. A spokesman for London Higher said: "We would be pleased to work with any initiatives that give support to students from poorer backgrounds to pursue their studies."

The mayor said: "I am concerned it will have a significant impact on lots of young people in London … it is important that we keep young people in school, not just so they receive an education but so they don't get sucked into crime."

A spokesman for Johnson's election campaign said on Thursday: "Ken Livingstone is at it again, making yet another un-costed, un-funded promise. He has already been forced to admit that if London's councils don't stump up the cash, City Hall will have to.

"This means raising City Hall's council tax, which given Mr Livingstone's record of raising it by 152% while mayor, costing the average London household £964, must be his plan."

The spokesman said Johnson was committed to keeping free travel for students, supporting apprenticeships and paid internships.

A spokesman for the Association of Colleges, which represents further education and sixth form colleges, said greater London had seen the steepest decline in the enrolment of 16- to 18-year-olds of any region.

"AoC is concerned about the evidence of the impact that the removal of the EMA has had on the ability of London's 16-year-olds to access the right courses," the spokesman said.

Evidence on the impact of withdrawing EMA is mixed. An AoC survey last year showed 49% of colleges nationally had seen a decline in student numbers, but 42% had an increase and the other colleges were stable. Figures published by the Department for Education last week show that the proportion of 16- to 18-year-olds who are out of school or training has remained stable year-on-year.

Responding to the Labour announcement, James Mills from the Save EMA campaign said: "This is great news for tens of thousands of the poorest teenagers in London; it means that they can once again take education as far as their ability lets them and not their ability to pay.

"This will not only set down a marker for other mayoral contests across the country, but has shown it is not about money, but about priorities when it comes to down whether teenagers should have EMA payments."